OreTools[Utility] - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Algebra : Skew Polynomials : OreTools : OreTools/Utility/Coefficient

OreTools[Utility]

  

Coefficient

  

return the coefficient of a specific power in an Ore polynomial

  

Coefficients

  

return the coefficient sequence of an Ore polynomial

  

Degree

  

return the degree of an Ore polynomial with respect to the noncommutative indeterminate

  

LeadingCoefficient

  

return the leading coefficient of an Ore polynomial

  

LowDegree

  

return the degree of the least power with nonzero coefficient

  

RandOrePoly

  

return a random Ore polynomial

  

TrailingCoefficient

  

return the trailing coefficient of an Ore Polynomial

  

VariableDegree

  

return the maximal degree of the coefficients of an Ore Polynomial in the variable in an Ore algebra

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Coefficient(Poly, n)

Coefficients(Poly)

Degree(Poly)

LeadingCoefficient(Poly)

LowDegree(Poly)

RandOrePoly(A, opts)

TrailingCoefficient(Poly)

VariableDegree(Poly, A)

Parameters

Poly

-

Ore polynomial; to define an Ore polynomial, see OreTools/OrePoly

n

-

non-negative integer

A

-

Ore algebra

opts

-

options

Description

• 

The Coefficient(Poly, n) calling sequence returns the coefficient of the nth power of the noncommutative indeterminate in Poly.

• 

The Coefficients(Poly) calling sequence returns the sequence of coefficients of Poly.

• 

The Degree(Poly) calling sequence returns the degree of Poly with respect to the noncommutative indeterminate.

• 

The LeadingCoefficient(Poly)] calling sequence returns the leading coefficient of Poly.

• 

The LowDegree(Poly) calling sequence returns the trailing degree of Poly.

• 

The RandOrePoly(A) calling sequence returns a random Ore polynomial in the Ore algebra A.

  

The first argument A specifies the ring in which the polynomial is to be generated. The possible options are:

  

coeffs - Generate the coefficients

  

terms - Number of terms in the noncommutative indeterminate

  

degree - Degree on the noncommutative indeterminate

• 

The TrailingCoefficient(Poly) calling sequence returns the trailing coefficient of A.

• 

The VariableDegree(Poly, A) calling sequence returns the maximal degree of coefficients of Poly with respect to the variable in A.  Note that the coefficients of Poly are supposed to be polynomials in the variable.

• 

For a brief review of pseudo-linear algebra (also known as Ore algebra), see OreAlgebra.

Examples

withOreTools:

withOreTools[Utility]:

Poly'OrePoly'0,2n1,0,1n

Poly:=OrePoly0,2n1,0,1n

(1)

CoefficientPoly,1

2n1

(2)

CoefficientPoly,6

0

(3)

CoefficientsPoly

0,2n1,0,1n

(4)

DegreePoly

3

(5)

Degree'OrePoly'0

∞

(6)

LeadingCoefficientPoly

1n

(7)

LowDegreePoly

1

(8)

LowDegree'OrePoly'0

∞

(9)

TrailingCoefficientPoly

2n1

(10)

TrailingCoefficient'OrePoly'0

0

(11)

ASetOreRingn,'shift':

PolyRandOrePolyA

Poly:=OrePoly72n5+37n423n3+87n2+44n+29,50n5+23n4+75n392n2+6n+74,17n575n410n37n240n+42,10n5+62n482n3+80n244n+71,62n4+97n373n24n83,7n5+22n455n394n2+87n56

(12)

DegreePoly

5

(13)

VariableDegreePoly,A

5

(14)

VariableDegree'OrePoly'0,A

∞

(15)

BSetOreRingx,'differential':

CRandOrePolyB,coeffs=polynomdegree=3,terms=2,terms=2,degree=10

C:=OrePoly0,0,0,0,40x381x,11+95x

(16)

VariableDegreeC,B

3

(17)

FSetOreRingx,q,'qshift':

Utility[RandOrePoly]F,coeffs=ratpolydegnum=1,degden=2,terms=2,degree=5,terms=3,degree=10

OrePoly0,87q+47x908848q,0,16q+30x2772qx96,0,0,0,0,51q+77x+9528qx+55q

(18)

See Also

OreTools

OreTools/OreAlgebra

OreTools/SetOreRing

OreTools[Utility]

randpoly

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam